Topic 7 - Inferential Stats Pt.2

what are inferential statistics

procedures for deciding whether sample data represent a particular relationship in the population 

parametric statistics

inferential procedures that require certain assumptions about the raw score population represented by the sample; used when we compute the mean

nonparametric statistics

inferential procedures that do not require stringent assumptions about the raw score population represented by the sample; used with the median and mode 

experimental hypotheses 

two statements describing the predicted relationship that may or may not be demonstrated by a study 

predicted relationship

manipulating the independent variable will have the expected influence on dependent scores

what is the second hypothesis for?

state that we will NOT demonstrate the predicted relationship in the population

a two-tailed test

used when we do not predict the direction in which dependent scores will change

a one tailed test 

when we do predict the direction in which dependent scores will change 

statistical hypothesis

statements that describe the population parameters the sample stats represent if the predicted relationship exists or does not exist

• alternative hypothesis

• null hypothesis

Alternative hypothesis (H(a)) 

the hypothesis describing the population parameters the sample data represent if the predicted relationship does exist in nature 

null hypothesis (H(0))

The hypothesis describing the population parameters the sample data represent if the predicted relationship does not exist in nature

statistical hypothesis testing

a method of statistical inference used to decide whether the data provide sufficient evidence to reject a particular hypothesis 

what are the four assumptions of the z-test

1. we have randomly selected one sample

2. the dependent variable is at least approx. normally distributed in the population and involves an interval or ratio scale

3. we know the mean of the population of raw scores under another condition of the independent variable

4. we know the true standard deviation of the population described by the null hypothesis

alpha α<.05

the greek letter that symbolizes the criterion probability

the risk of committing a type 1 error

anything less than alpha we count as rare event that rejects the null hypothesis 

what is a z-test

the parametric procedure used in a single sample experiment when the standard deviation of the raw score population is known

region of rejection

located in each tail of the distribution, marked by the critical values of +- 1.96

significant

describes results that are unlikely to result from sampling error when the predicted relationship does not exist; it indicates rejection of the null hypothesis

nonsignificant 

describes results that are likely to result from sampling error when the predicted relationship does not exist; it indicates failure to reject the null hypothesis 

what is the risk to using one-tailed tests

it is only significant if it lies beyond z AND has the same sign

when to use a one-tailed test example

For example, if testing whether a new drug is more effective than an existing one, the hypothesis would focus only on improvement.

• This test allocates the entire significance level (e.g., 5%) to one tail, providing more power to detect an effect in the specified direction.

• However, it disregards the possibility of an effect in the opposite direction, which can be a limitation in certain scenarios.

when to use a two-tailed test example

For instance, testing whether a new policy affects farmers' loans could consider both increases and decreases.

• This test is more conservative, as it accounts for effects in both directions, dividing the significance level (e.g., 2.5% in each tail).

• It is suitable when the direction of the effect is unknown or when both directions are of interest.

type 1 error

rejecting H(0) when H(0) is true

type 2 error

retaining H(0) when H(0) is really false

power

the probability that we will reject H(0) when it is false

and correctly conclude that the sample data represent a real relationship

• i.e. the probability of NOT making a type 2 error

random sampling

selects a sample from a population such that each individual has an equal and independent chance of being selected 

sampling error

reflects that fact that the statistics of randomly drawn samples will deviate from the corresponding population parameters

random sampling variability

reflects the fact that owing to chance two random samples drawn from the same population will have diff stats

what is step one of null hypothesis significance testing

start with statistical null model

what is step two of null hypothesis significance testing

identify an appropriate sampling distribution of our null model 

what is step three of null hypothesis significance testing

calculate probabilities of observing samples of data under the null

what is step four of null hypothesis significance testing

collect random sample data from the population

what is step five of null hypothesis significance testing

the rare event rule a<.05

what is the rare event rule 

when the probability of an event occurring is low but it happens anyway

P-values

the probability of observing data as extreme or more extreme than what we actually observed- if the null hypothesis were true

quantified how rare our observed result would be if the null hypothesis were true

what are the 5 steps of hypothesis testing

1. state the hypothesis (null and alternative)

2. define the comparison

3. set the decision criterion - what counts as a rare event

4. compute the test statistic

5. make a decision